The 23-year-old is a product of Barcelona’s academy and he secured a return to the Nou Camp this summer following spells with AC Milan and Everton.
Neymar’s recent departure to Paris Saint-Germain has provided Deulofeu with the opportunity to stake a claim for a starting spot ahead of the new La Liga campaign.
The winger was picked to start against Brazilian side Chapecoense in the Joan Gamper Trophy earlier this week and Valverde was happy with his performance.
However, Valverde is keen to see how his new recruit performs in a high-pressure situation as they prepare to face Real Madrid over two legs in the Spanish Super Cup.
Valverde said: "With Deulofeu, we only have his performance against Chapecoense to use as a reference.
"It's too early to judge his understanding with the other players, although I liked his performance in the Gamper Trophy. We'll see when we're faced by real difficulties."